# Question: Xiang Zhu a client of FinCorp Inc has phoned you

Xiang Zhu, a client of FinCorp Inc., has phoned you with a question. She has been reading a finance textbook and cannot understand how to use the binomial option pricing model to value a call option. The underlying stock is currently trading for $100. There is a 30-percent chance it will increase to $190 in one year, and a 70-percent chance it will fall to $85 in the same period. The risk-free rate is 10 percent. There is a call option with a strike price of $170, which according to the binomial model should have a value of $4.329. Xiang is confused because she calculates that if there is a 30-percent chance the call will be worth $20 and a 70-percent chance it will be worth zero, the expected value should be $6. Why is it only worth $4.329?

a. Demonstrate that if the call was trading for $6, there would be an arbitrage opportunity.

b. Calculate the risk-neutral probabilities.

c. Calculate the expected present value of the call option using the risk-neutral probabilities.

d. Why can we value options as if the investors are risk neutral?

a. Demonstrate that if the call was trading for $6, there would be an arbitrage opportunity.

b. Calculate the risk-neutral probabilities.

c. Calculate the expected present value of the call option using the risk-neutral probabilities.

d. Why can we value options as if the investors are risk neutral?

## Relevant Questions

Assume stock XYZ does not pay dividends and has a market value of $98 per share. There is a 60-percent chance that the stock will trade for $130 in one year, and a 40-percent chance that it will trade for $55 in one year. ...1. Which of the following statements about IRR and NPV is incorrect?a. NPV and IRR yield the same ranking when evaluating projects.b. NPV assumes that cash flows are reinvested at the cost of capital of the firm.c. A project ...Using projects A to F in Table 1, construct BigCo’s investment opportunity schedule. If BigCo has $8,000 available for investment, which projects should it undertake. Justify your recommendations to the CEO ofBigCo.Given the following: Project A: CF0 = –$23,000; CF1 = $6,000; CF2 = $9,000; CF3 = $15,600Project B: CF0 = –$20,000; CF1 = $4,000; CF2 = $8,000; CF3 = $15,000What is the crossover rate (r)?A project has an NPV of $50,000. Calculate the cost of capital of this project if it generates the following cash flows for six years after an initial investment of $200,000:Year 1: $50,000Year 2: $50,000Year 3: $30,000Year ...Post your question